Using remainder theorem- find the remainder when-2 x3-5 x2-9 x-8 is divided by x-3

We have: x 3=0 #8658;x=3 By the remainder theorem, we know that when nbsp;f(x) is divided by (x nbsp; 3), the remainder is nbsp;f(3). Thus, we have: fx ...

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Standard IX

Mathematics

Remainder Theorem

Using remaind...

Question

Using remainder theorem, find the remainder when:
(2x³ − 5x² + 9x − 8) is divided by (x − 3)

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Solution

We have:
$x - 3 = 0 \Rightarrow x = 3$
By the remainder theorem, we know that when f(x) is divided by (x $-$ 3), the remainder is f(3).
Thus, we have:
$f (x) = (2 x^{3} - 5 x^{2} + 9 x - 8) ∴ f (3) = (2 \times 3^{3} - 5 \times 3^{2} + 9 \times 3 - 8) = (54 - 45 + 27 - 8) = 28$
Hence, the required remainder is 28.

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Using remainder theorem, find the remainder when: (2x3 − 5x2 + 9x − 8) is divided by (x − 3)

We have: x-3=0⇒x=3 By the remainder theorem, we know that when f(x) is divided by (x - 3), the remainder is f(3). Thus, we have: fx=2x3-5x2+9x-8∴ f3=2×33-5×32+9×3-8 =54-45+27-8 =28 ​Hence, the required remainder is 28.

Using remainder theorem, find the remainder when:
(2x³ − 5x² + 9x − 8) is divided by (x − 3)